Integrating Using Arctan

  • Thread starter jumbogala
  • Start date
  • #1
423
2

Homework Statement


Integrate
1/(x2 +11x +29)

Homework Equations





The Attempt at a Solution


I'm doing something wrong, but can't figure out what...

Complete the square so that the denominator equals (x+2)2+25

Then divide by 25: ((x+2)2)/25 + 1

Move that 25 into the squared part: ((x+2)/5)2+1

Substitute the squared part for u.

Find du/dx = 1/5, and therefore 5du=dx

Now we have 5*(integral sign) du / (u2+1)

This gives 5arctan(u)+C --> substitute u back for what you had before.

But the answer is 1/5arctan(u). Where did I go wrong?
 
Last edited:

Answers and Replies

  • #2
623
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When you "divide by 25", where does that 25 go?
 
  • #3
423
2
Oops, I was focusing so much on the denominator, I forgot about the numerator. This is what happens when yiou do math late at night, haha.

Thanks!
 
  • #4
Dick
Science Advisor
Homework Helper
26,260
619
You can't just divide by something and expect the answer to be unchanged. Once you have 1/((x+5)^2+25) why not just substitute (x+5)=5*u?
 
  • #5
djeitnstine
Gold Member
614
0
how about x+2 = 5tanu to make life easier
 

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